Abstract

This correspondence presents a derivation of an alternate set of equations for determination of the optimal feedback gain matrix for the time-dependent linear regulator problem. In contrast to the usual Riccati equation approach, the new system is composed of onlynmequations, wheremis the number of systems input terminals. As payment for this reduction in number of equations, however, the new system is not entirely general, being restricted to constant control matricesG, with arbitrary dynamics and cost matricesFandQ, respectively.